Lorentz Meets Fano in Spectral Line Shapes: A Universal Phase and Its Laser Control

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Science  10 May 2013:
Vol. 340, Issue 6133, pp. 716-720
DOI: 10.1126/science.1234407

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A Phase for Fano

In spectroscopy, samples placed between a steady light source and a detector are characterized based on the relative intensities of light absorbed at different frequencies. Temporal behavior—the relaxation of a photoexcited state—can be indirectly inferred from the absorption band shapes. The advent of ultrafast laser technology has enabled increasingly sophisticated measurements directly in the time domain. Ott et al. (p. 716; see the Perspective by Lin and Chu) present an analytical framework to account for asymmetric band shapes, termed Fano profiles, on the basis of a phase shift in the temporal dipole response.


Symmetric Lorentzian and asymmetric Fano line shapes are fundamental spectroscopic signatures that quantify the structural and dynamical properties of nuclei, atoms, molecules, and solids. This study introduces a universal temporal-phase formalism, mapping the Fano asymmetry parameter q to a phase ϕ of the time-dependent dipole response function. The formalism is confirmed experimentally by laser-transforming Fano absorption lines of autoionizing helium into Lorentzian lines after attosecond-pulsed excitation. We also demonstrate the inverse, the transformation of a naturally Lorentzian line into a Fano profile. A further application of this formalism uses quantum-phase control to amplify extreme-ultraviolet light resonantly interacting with He atoms. The quantum phase of excited states and its response to interactions can thus be extracted from line-shape analysis, with applications in many branches of spectroscopy.

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